International Journal of Theoretical Physics

, Volume 52, Issue 8, pp 2657–2673 | Cite as

Harmonic and Wave Maps Coupled with Einstein’s Gravitation



In this paper we discuss the coupled dynamics, following from a suitable Lagrangian, of a harmonic or wave map ϕ and Einstein’s gravitation described by a metric g. The main results concern energy conditions for wave maps, harmonic maps from warped product manifolds, and wave maps from wave-like Lorentzian manifolds.


Harmonic map Wave map Energy conditions 



Former discussions and cooperations with T. Hirschmann and T. Deck are gratefully acknowledged. We thank the professors G. Huisken and A.D. Rendall for inspiring discussions.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Universität GraeifswaldInstitut für Mathematik und informatikGreifswaldGermany
  2. 2.Mathematics Department, Faculty of ScienceKing Abdulaziz UniversityJeddahKSA
  3. 3.Mathematics Department, Faculty of ScienceMinia UniversityEl-MiniaEgypt

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